Proof of Work is the system by which most cryptocurrencies, including Bitcoin, manage their blockchains. Through a process known as mining, individuals contribute processing power to solve difficult, arbitrary calculations as well as to validate calculations to determine what the next block in the blockchain should be. Whenever a new block is added to the chain, whoever was lucky enough to be the person that created that block is rewarded with some amount of currency.

The difficulty of these calculations can be determined by the developers behind the currency to control the rate at which new coins are dispersed into the economy. The reason for the difficult calculations is to secure the network by making it difficult for an attacker to start adding invalid blocks to the universally accepted chain — in this system, the attacker would need to generate over 50% of the processing power in the entire network to have their malicious validation be accepted.

A higher-level way to think about this is that processing power is what creates scarcity and is proportional to the odds of you getting the next reward. This has the unfortunate side-effect of giving a disproportionate amount of power, in regards to both reward and blockchain validation, to miners that control a large portion of the mining hashrate.